311 research outputs found
Dynamic Scaling in a 2+1 Dimensional Limited Mobility Model of Epitaxial Growth
We study statistical scale invariance and dynamic scaling in a simple
solid-on-solid 2+1 - dimensional limited mobility discrete model of
nonequilibrium surface growth, which we believe should describe the low
temperature kinetic roughening properties of molecular beam epitaxy. The model
exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling
properties similar to that found in the corresponding 1+1 - dimensional
problem. Using large-scale simulations we obtain the relevant scaling
exponents, and compare with continuum theories.Comment: 5 pages, 4 ps figures included, RevTe
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series
of the form , where the are independent and identically
distributed random variables and is a constant drift. For very small and
very large drift velocities, we investigate the asymptotic behavior of the
probability of a record occurring in the th step and the
probability that all entries are records, i.e. that . Our work is motivated by the analysis of temperature time series in
climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure
Non-neutral theory of biodiversity
We present a non-neutral stochastic model for the dynamics taking place in a
meta-community ecosystems in presence of migration. The model provides a
framework for describing the emergence of multiple ecological scenarios and
behaves in two extreme limits either as the unified neutral theory of
biodiversity or as the Bak-Sneppen model. Interestingly, the model shows a
condensation phase transition where one species becomes the dominant one, the
diversity in the ecosystems is strongly reduced and the ecosystem is
non-stationary. This phase transition extend the principle of competitive
exclusion to open ecosystems and might be relevant for the study of the impact
of invasive species in native ecologies.Comment: 4 pages, 3 figur
Derivation of continuum stochastic equations for discrete growth models
We present a formalism to derive the stochastic differential equations (SDEs)
for several solid-on-solid growth models. Our formalism begins with a mapping
of the microscopic dynamics of growth models onto the particle systems with
reactions and diffusion. We then write the master equations for these
corresponding particle systems and find the SDEs for the particle densities.
Finally, by connecting the particle densities with the growth heights, we
derive the SDEs for the height variables. Applying this formalism to discrete
growth models, we find the Edwards-Wilkinson equation for the symmetric
body-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equation
for the asymmetric BCSOS model and the generalized restricted solid-on-solid
(RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOS
model. In addition to the consistent forms of equations for growth models, we
also obtain the coefficients associated with the SDEs.Comment: 5 pages, no figur
Evolution in random fitness landscapes: the infinite sites model
We consider the evolution of an asexually reproducing population in an
uncorrelated random fitness landscape in the limit of infinite genome size,
which implies that each mutation generates a new fitness value drawn from a
probability distribution . This is the finite population version of
Kingman's house of cards model [J.F.C. Kingman, \textit{J. Appl. Probab.}
\textbf{15}, 1 (1978)]. In contrast to Kingman's work, the focus here is on
unbounded distributions which lead to an indefinite growth of the
population fitness. The model is solved analytically in the limit of infinite
population size and simulated numerically for finite . When
the genome-wide mutation probability is small, the long time behavior of
the model reduces to a point process of fixation events, which is referred to
as a \textit{diluted record process} (DRP). The DRP is similar to the standard
record process except that a new record candidate (a number that exceeds all
previous entries in the sequence) is accepted only with a certain probability
that depends on the values of the current record and the candidate. We develop
a systematic analytic approximation scheme for the DRP. At finite the
fitness frequency distribution of the population decomposes into a stationary
part due to mutations and a traveling wave component due to selection, which is
shown to imply a reduction of the mean fitness by a factor of compared to
the limit.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday.
Submitted to JSTAT. Error in Section 3.2 was correcte
Anisotropic Colossal Magnetoresistance Effects in Fe_{1-x}Cu_xCr_2S_4
A detailed study of the electronic transport and magnetic properties of
FeCuCrS () on single crystals is presented. The
resistivity is investigated for K in magnetic fields up to
14 Tesla and under hydrostatic pressure up to 16 kbar. In addition
magnetization and ferromagnetic resonance (FMR) measurements were performed.
FMR and magnetization data reveal a pronounced magnetic anisotropy, which
develops below the Curie temperature, , and increases strongly
towards lower temperatures. Increasing the Cu concentration reduces this
effect. At temperatures below 35 K the magnetoresistance, , exhibits a strong dependence on the direction of the
magnetic field, probably due to an enhanced anisotropy. Applying the field
along the hard axis leads to a change of sign and a strong increase of the
absolute value of the magnetoresistance. On the other hand the
magnetoresistance remains positive down to lower temperatures, exhibiting a
smeared out maximum with the magnetic field applied along the easy axis. The
results are discussed in the ionic picture using a triple-exchange model for
electron hopping as well as a half-metal utilizing a band picture.Comment: some typos correcte
Reaction Diffusion Models in One Dimension with Disorder
We study a large class of 1D reaction diffusion models with quenched disorder
using a real space renormalization group method (RSRG) which yields exact
results at large time. Particles (e.g. of several species) undergo diffusion
with random local bias (Sinai model) and react upon meeting. We obtain the
large time decay of the density of each specie, their associated universal
amplitudes, and the spatial distribution of particles. We also derive the
spectrum of exponents which characterize the convergence towards the asymptotic
states. For reactions with several asymptotic states, we analyze the dynamical
phase diagram and obtain the critical exponents at the transitions. We also
study persistence properties for single particles and for patterns. We compute
the decay exponents for the probability of no crossing of a given point by,
respectively, the single particle trajectories () or the thermally
averaged packets (). The generalized persistence exponents
associated to n crossings are also obtained. Specifying to the process or A with probabilities , we compute exactly the exponents
and characterizing the survival up to time t of a domain
without any merging or with mergings respectively, and and
characterizing the survival up to time t of a particle A without
any coalescence or with coalescences respectively.
obey hypergeometric equations and are numerically surprisingly close to pure
system exponents (though associated to a completely different diffusion
length). Additional disorder in the reaction rates, as well as some open
questions, are also discussed.Comment: 54 pages, Late
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